Fringe visibility of exotic trajectories for matter waves in a double-slit experiment.

Abstract

We theoretically study the fringe visibility of exotic looped trajectories in double-slit experiments with matter waves. We consider the relative intensity at x=0x=0 as a function of the time-of-flight from the double-slit to the screen inside the interferometer. This allows us to define a fringe visibility associated with the contribution to the interference pattern given by exotic looped trajectories. We demonstrate that the Sorkin parameter is given in terms of this visibility and of the axial phases which include the Gouy phase. Thus, the effect of exotic looped trajectories can be attested by measuring deviations from unity for the fringe visibility. We show that the effect of exotic trajectories can be increased by adjusting the parameters of the double-slit apparatus in the Fresnel regime.